There are a few things to look for that might help in determining if a tree is a hazard:
1. Is there dieback in the canopy (sections of dead leaves)?
2. Is the ground around the base of the tree mounded near the base?
3. Have you observed fungus conks or mushrooms growing near the base of the tree during spring?
4. Is there ants on or around the tree?
5. Do you notice any cavities (openings) into the trunk?

As trees age a column of decay will form in the center. This is a normal part of tree development. It is not uncommon for mature trees to have a hollow section in the middle of the trunk. The important issue that needs to be determined is how much of the trunk is hollow (decayed) and how much is alive? Is the alive wood structurally sound enough to support the weight of the tree?

This is a situation where you would want to hire an arborist to perform a visual tree assessment (VTA). Arborists have a whole series of criteria that they will use in determining if the tree is structurally sound. They also have tools that will allow them to determine how much of the tree is alive and how much is dead called a resistogragh.